sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A383829 | Number of medial involutory racks of order n, up to isomorphism. | [
"1",
"1",
"2",
"5",
"12",
"38",
"168",
"850",
"6090"
]
| [
"nonn",
"hard",
"more"
]
| 8 | 0 | 3 | [
"A165200",
"A176077",
"A177886",
"A178432",
"A179010",
"A181769",
"A181770",
"A181771",
"A193024",
"A196111",
"A198147",
"A225744",
"A226172",
"A226173",
"A226174",
"A226193",
"A236146",
"A242044",
"A242275",
"A243931",
"A248908",
"A254434",
"A257351",
"A374939",
"A374942",
"A374943",
"A374944",
"A374945",
"A374946",
"A374947",
"A383144",
"A383145",
"A383146",
"A383828",
"A383829",
"A383830",
"A383831"
]
| null | Luc Ta, May 11 2025 | 2025-05-16T14:33:54 | oeisdata/seq/A383/A383829.seq | 460ac82eddbb39c146b5c5fa7c1f0cfe |
A383830 | Number of Legendrian quandles of order n, up to isomorphism. | [
"1",
"1",
"2",
"5",
"15",
"54",
"240",
"1306",
"9477"
]
| [
"nonn",
"hard",
"more"
]
| 8 | 0 | 3 | [
"A165200",
"A176077",
"A177886",
"A178432",
"A179010",
"A181769",
"A181770",
"A181771",
"A193024",
"A196111",
"A198147",
"A225744",
"A226172",
"A226173",
"A226174",
"A226193",
"A236146",
"A242044",
"A242275",
"A243931",
"A248908",
"A254434",
"A257351",
"A374939",
"A374942",
"A374943",
"A374944",
"A374945",
"A374946",
"A374947",
"A383144",
"A383145",
"A383146",
"A383828",
"A383829",
"A383830",
"A383831"
]
| null | Luc Ta, May 11 2025 | 2025-05-16T14:34:27 | oeisdata/seq/A383/A383830.seq | a0590ca8272147628d6cd382da42ad44 |
A383831 | Number of medial Legendrian quandles of order n, up to isomorphism. | [
"1",
"1",
"2",
"5",
"14",
"48",
"219",
"1207",
"9042"
]
| [
"hard",
"more",
"nonn"
]
| 11 | 0 | 3 | [
"A165200",
"A176077",
"A177886",
"A178432",
"A179010",
"A181769",
"A181770",
"A181771",
"A193024",
"A196111",
"A198147",
"A225744",
"A226172",
"A226173",
"A226174",
"A226193",
"A236146",
"A242044",
"A242275",
"A243931",
"A248908",
"A254434",
"A257351",
"A374939",
"A374942",
"A374943",
"A374944",
"A374945",
"A374946",
"A374947",
"A383144",
"A383145",
"A383146",
"A383828",
"A383830",
"A383831"
]
| null | Luc Ta, May 16 2025 | 2025-05-16T09:44:45 | oeisdata/seq/A383/A383831.seq | e1d8a98ffb7c1b03d48c68f57dd5c11b |
A383833 | Area of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"0",
"6",
"84",
"546",
"2310",
"7440",
"19866",
"46284",
"97236",
"188370",
"341880",
"588126",
"967434",
"1532076",
"2348430",
"3499320",
"5086536",
"7233534",
"10088316",
"13826490",
"18654510",
"24813096",
"32580834",
"42277956",
"54270300",
"68973450",
"86857056",
"108449334",
"134341746",
"165193860",
"201738390"
]
| [
"nonn",
"easy",
"changed"
]
| 13 | 0 | 2 | [
"A000217",
"A002061",
"A058919",
"A336535",
"A383833",
"A383834"
]
| null | Miguel-Ángel Pérez García-Ortega, May 11 2025 | 2025-07-13T17:21:48 | oeisdata/seq/A383/A383833.seq | 9713dab2f6172eb1806559f127d48329 |
A383834 | Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"1",
"7",
"31",
"97",
"241",
"511",
"967",
"1681",
"2737",
"4231",
"6271",
"8977",
"12481",
"16927",
"22471",
"29281",
"37537",
"47431",
"59167",
"72961",
"89041",
"107647",
"129031",
"153457",
"181201",
"212551",
"247807",
"287281",
"331297",
"380191",
"434311",
"494017",
"559681",
"631687",
"710431",
"796321",
"889777",
"991231",
"1101127",
"1219921",
"1348081"
]
| [
"nonn",
"easy",
"changed"
]
| 18 | 0 | 2 | [
"A000217",
"A002061",
"A006007",
"A058919",
"A336535",
"A383833",
"A383834"
]
| null | Miguel-Ángel Pérez García-Ortega, May 11 2025 | 2025-07-13T17:25:49 | oeisdata/seq/A383/A383834.seq | c2e27056388536e9db18378357f5e29b |
A383835 | Number of permutations of [n] whose compositional square is the identity permutation or its reverse. | [
"1",
"1",
"2",
"4",
"12",
"28",
"76",
"232",
"776",
"2632",
"9496",
"35696",
"140272",
"568624",
"2390480",
"10349536",
"46208416",
"211800992",
"997313824",
"4809701440",
"23758694336",
"119952723136",
"618884638912",
"3257843882624",
"17492191242880",
"95680444425856",
"532985208200576",
"3020676745975552"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 3 | [
"A000085",
"A000142",
"A037224",
"A383835"
]
| null | Darío Clavijo, May 11 2025 | 2025-05-19T17:58:14 | oeisdata/seq/A383/A383835.seq | f029f607612b6725aaae699067a59e12 |
A383836 | Integers k such that d*2^k + k/d is prime for some divisor d of k. | [
"1",
"3",
"5",
"6",
"9",
"10",
"15",
"21",
"22",
"28",
"39",
"66",
"75",
"81",
"89",
"105",
"108",
"111",
"141",
"165",
"166",
"190",
"196",
"317",
"340",
"357",
"459",
"462",
"483",
"525",
"564",
"568",
"573",
"701",
"735",
"737",
"792",
"869",
"1185",
"1311",
"1480",
"1647",
"1794",
"1881",
"2145",
"2405",
"2508",
"2766",
"3081",
"3201",
"3225",
"3243",
"4260",
"4713",
"5369",
"5795",
"5985"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A057663",
"A161904",
"A383473",
"A383836"
]
| null | Juri-Stepan Gerasimov, May 11 2025 | 2025-05-28T18:09:56 | oeisdata/seq/A383/A383836.seq | 1615aa63f4ff97dc0cdeb44e68e2bd83 |
A383837 | a(n) = (3*n)!/n! * [x^(3*n)] sinh(x)^n. | [
"1",
"1",
"16",
"820",
"87296",
"15857205",
"4390088704",
"1721255653656",
"907673633095680",
"619593964021650475",
"531571294549842067456",
"559896149105493602658256",
"710322778732936488128872448",
"1068386732538408106621063668220",
"1879866814874817967233600382304256"
]
| [
"nonn"
]
| 20 | 0 | 3 | [
"A298851",
"A381459",
"A381512",
"A383837"
]
| null | Seiichi Manyama, May 11 2025 | 2025-05-17T05:03:30 | oeisdata/seq/A383/A383837.seq | 6bf268ae1188201cb4a7adf838ba2065 |
A383838 | Expansion of 1/((1-x) * (1-4*x) * (1-9*x) * (1-16*x)). | [
"1",
"30",
"627",
"11440",
"196053",
"3255330",
"53157079",
"860181300",
"13850000505",
"222384254950",
"3565207699131",
"57106865357880",
"914281747641757",
"14633655168987690",
"234184807922193183",
"3747373855152257980",
"59961734043737254209",
"959421515974412698350",
"15351048197153778821635"
]
| [
"nonn",
"easy"
]
| 25 | 0 | 2 | [
"A002451",
"A269945",
"A383838"
]
| null | Seiichi Manyama, May 11 2025 | 2025-05-12T11:53:55 | oeisdata/seq/A383/A383838.seq | 2d48021913a346d6c1356861b87aa918 |
A383839 | a(n) = [x^n] 1/(1 - n*x) * Product_{k=0..n-1} (1 + k*x)/(1 - k*x). | [
"1",
"1",
"10",
"177",
"4576",
"156145",
"6627006",
"336562177",
"19906794496",
"1344082891761",
"102012257669950",
"8597688151223281",
"796733925564191616",
"80516951813773009249",
"8812696026991760928766",
"1038540275078155878285825",
"131107274213106172807069696",
"17652158052761888943436783009"
]
| [
"nonn"
]
| 20 | 0 | 3 | [
"A350366",
"A383767",
"A383839"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-14T10:51:00 | oeisdata/seq/A383/A383839.seq | 1cddffd920cf8cdd42c2d42b42106113 |
A383840 | Expansion of 1/((1-x) * (1-4*x) * (1-9*x) * (1-16*x) * (1-25*x)). | [
"1",
"55",
"2002",
"61490",
"1733303",
"46587905",
"1217854704",
"31306548900",
"796513723005",
"20135227330075",
"506945890951006",
"12730754139133030",
"319183135225967507",
"7994212035818175365",
"200089485703376577308",
"5005984516439566690680",
"125209574645032904521209"
]
| [
"nonn",
"easy"
]
| 23 | 0 | 2 | [
"A269945",
"A383838",
"A383840"
]
| null | Seiichi Manyama, May 11 2025 | 2025-05-12T11:53:59 | oeisdata/seq/A383/A383840.seq | 682a5bb6bffed53455d86c3a340facf1 |
A383841 | Expansion of 1/((1-x) * (1-2*x) * (1-3*x))^2. | [
"1",
"12",
"86",
"480",
"2307",
"10044",
"40792",
"157440",
"584693",
"2107596",
"7420218",
"25634880",
"87207559",
"292924668",
"973531964",
"3206704800",
"10482373305",
"34042285260",
"109930177630",
"353238247200",
"1130137576331",
"3601849005372",
"11440208166816",
"36225346150080",
"114391746903037",
"360325587293004"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 2 | [
"A000392",
"A045618",
"A383841",
"A383843"
]
| null | Seiichi Manyama, May 12 2025 | 2025-05-12T10:01:45 | oeisdata/seq/A383/A383841.seq | 201099d7f5543a000cecf68566d58394 |
A383842 | Expansion of 1/((1-x) * (1-2*x) * (1-3*x) * (1-4*x))^2. | [
"1",
"20",
"230",
"2000",
"14627",
"95060",
"567240",
"3174400",
"16904053",
"86549620",
"429352330",
"2075659600",
"9822847079",
"45665147700",
"209129160300",
"945597624000",
"4229196800505",
"18738054705300",
"82347219011950",
"359322115058000",
"1558151553849131",
"6719660438870420",
"28838298857544080"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 2 | [
"A000453",
"A383842",
"A383843"
]
| null | Seiichi Manyama, May 12 2025 | 2025-05-12T10:01:49 | oeisdata/seq/A383/A383842.seq | 2b43abe4519edd47a98c21749ccd4331 |
A383843 | Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of 1/Product_{j=0..k} (1 - j*x)^2. | [
"1",
"1",
"0",
"1",
"2",
"0",
"1",
"6",
"3",
"0",
"1",
"12",
"23",
"4",
"0",
"1",
"20",
"86",
"72",
"5",
"0",
"1",
"30",
"230",
"480",
"201",
"6",
"0",
"1",
"42",
"505",
"2000",
"2307",
"522",
"7",
"0",
"1",
"56",
"973",
"6300",
"14627",
"10044",
"1291",
"8",
"0",
"1",
"72",
"1708",
"16464",
"65002",
"95060",
"40792",
"3084",
"9",
"0",
"1",
"90",
"2796",
"37632",
"227542",
"587580",
"567240",
"157440",
"7181",
"10",
"0"
]
| [
"nonn",
"tabl"
]
| 22 | 0 | 5 | [
"A000007",
"A000027",
"A045618",
"A106800",
"A287532",
"A350376",
"A383841",
"A383842",
"A383843",
"A383880"
]
| null | Seiichi Manyama, May 12 2025 | 2025-05-15T08:17:09 | oeisdata/seq/A383/A383843.seq | 72c597c1686a36bb0bceee65c12cf334 |
A383844 | a(n) is the number of occurences of n in A024934. | [
"3",
"3",
"0",
"1",
"2",
"0",
"1",
"1",
"3",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"2",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1"
]
| [
"nonn"
]
| 29 | 0 | 1 | [
"A024934",
"A049802",
"A383327",
"A383844"
]
| null | Miles Englezou, May 12 2025 | 2025-05-28T19:00:41 | oeisdata/seq/A383/A383844.seq | fccb9ff56fcfbb189299ff0dd1d7d1c2 |
A383845 | Triangle T(n,k) read by rows: where T(n,k) is the number of the k-th eliminated person in the variation of the Josephus elimination process for n people, where the elimination pattern is eliminate-eliminate-skip. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"4",
"3",
"1",
"2",
"4",
"5",
"3",
"1",
"2",
"4",
"5",
"3",
"6",
"1",
"2",
"4",
"5",
"7",
"3",
"6",
"1",
"2",
"4",
"5",
"7",
"8",
"6",
"3",
"1",
"2",
"4",
"5",
"7",
"8",
"3",
"6",
"9",
"1",
"2",
"4",
"5",
"7",
"8",
"10",
"3",
"9",
"6",
"1",
"2",
"4",
"5",
"7",
"8",
"10",
"11",
"6",
"9",
"3",
"1",
"2",
"4",
"5",
"7",
"8",
"10",
"11",
"3",
"6",
"12",
"9",
"1",
"2",
"4",
"5",
"7",
"8",
"10",
"11",
"13",
"3",
"9",
"12",
"6"
]
| [
"nonn",
"tabl"
]
| 14 | 1 | 3 | [
"A001651",
"A006257",
"A383845",
"A383846",
"A383847",
"A384753"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, May 12 2025 | 2025-06-15T09:34:55 | oeisdata/seq/A383/A383845.seq | c1fa74ce93442a3c9ce4d8e9a2e55961 |
A383846 | A version of the Josephus problem: a(n) is the surviving integer under the eliminate-eliminate-skip version of the elimination process. | [
"1",
"2",
"3",
"3",
"3",
"6",
"6",
"3",
"9",
"6",
"3",
"9",
"6",
"12",
"9",
"15",
"12",
"18",
"15",
"3",
"18",
"6",
"21",
"9",
"24",
"12",
"27",
"15",
"3",
"18",
"6",
"21",
"9",
"24",
"12",
"27",
"15",
"30",
"18",
"33",
"21",
"36",
"24",
"39",
"27",
"42",
"30",
"45",
"33",
"48",
"36",
"51",
"39",
"54",
"42",
"3",
"45",
"6",
"48",
"9",
"51",
"12",
"54",
"15",
"57",
"18",
"60",
"21",
"63",
"24",
"66",
"27"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A001651",
"A006257",
"A337191",
"A381051",
"A383845",
"A383846",
"A383847"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, May 12 2025 | 2025-05-26T17:17:09 | oeisdata/seq/A383/A383846.seq | 0c06542e65c9bf03dda32c27f0016569 |
A383847 | Triangle T(n,k) read by rows, where row n is a permutation of the numbers 1 through n, such that if a deck of n cards is prepared in this order, and down-down-under dealing is used, then the resulting cards will be dealt in increasing order. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"4",
"3",
"1",
"2",
"5",
"3",
"4",
"1",
"2",
"5",
"3",
"4",
"6",
"1",
"2",
"6",
"3",
"4",
"7",
"5",
"1",
"2",
"8",
"3",
"4",
"7",
"5",
"6",
"1",
"2",
"7",
"3",
"4",
"8",
"5",
"6",
"9",
"1",
"2",
"8",
"3",
"4",
"10",
"5",
"6",
"9",
"7",
"1",
"2",
"11",
"3",
"4",
"9",
"5",
"6",
"10",
"7",
"8",
"1",
"2",
"9",
"3",
"4",
"10",
"5",
"6",
"12",
"7",
"8",
"11",
"1",
"2",
"10",
"3",
"4",
"13",
"5",
"6",
"11",
"7",
"8",
"12",
"9"
]
| [
"nonn",
"tabl"
]
| 8 | 1 | 3 | [
"A001651",
"A006257",
"A225381",
"A321298",
"A378635",
"A381050",
"A382528",
"A383845",
"A383846",
"A383847"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, May 12 2025 | 2025-05-23T16:06:14 | oeisdata/seq/A383/A383847.seq | 7736d1bc94cc735499b313e4fad0f1fd |
A383848 | In the binary representation of n, rotate left by the number of ones. | [
"0",
"1",
"1",
"3",
"1",
"6",
"3",
"7",
"1",
"6",
"10",
"13",
"3",
"14",
"7",
"15",
"1",
"6",
"10",
"28",
"18",
"13",
"21",
"27",
"3",
"14",
"22",
"29",
"7",
"30",
"15",
"31",
"1",
"6",
"10",
"28",
"18",
"44",
"52",
"57",
"34",
"13",
"21",
"58",
"37",
"27",
"43",
"55",
"3",
"14",
"22",
"60",
"38",
"29",
"45",
"59",
"7",
"30",
"46",
"61",
"15",
"62",
"31",
"63",
"1",
"6",
"10",
"28",
"18",
"44",
"52",
"120",
"34"
]
| [
"nonn",
"base",
"easy"
]
| 14 | 0 | 4 | [
"A006257",
"A007088",
"A383848",
"A383849",
"A383850"
]
| null | Paolo Xausa, May 13 2025 | 2025-05-14T14:09:07 | oeisdata/seq/A383/A383848.seq | 781833c4b70cc186ac5838ba18a2e20a |
A383849 | In the binary representation of n, rotate right by the number of ones. | [
"0",
"1",
"1",
"3",
"2",
"3",
"5",
"7",
"4",
"6",
"10",
"7",
"3",
"11",
"13",
"15",
"8",
"12",
"20",
"14",
"5",
"22",
"26",
"15",
"6",
"7",
"11",
"23",
"19",
"27",
"29",
"31",
"16",
"24",
"40",
"28",
"9",
"44",
"52",
"30",
"10",
"13",
"21",
"46",
"37",
"54",
"58",
"31",
"12",
"14",
"22",
"15",
"38",
"23",
"27",
"47",
"7",
"39",
"43",
"55",
"51",
"59",
"61",
"63",
"32",
"48",
"80",
"56",
"17",
"88",
"104",
"60",
"18"
]
| [
"nonn",
"base",
"easy"
]
| 10 | 0 | 4 | [
"A007088",
"A038572",
"A383848",
"A383849",
"A383850"
]
| null | Paolo Xausa, May 13 2025 | 2025-05-14T14:09:14 | oeisdata/seq/A383/A383849.seq | 20cfbb21039cd3cbb3ca0290f2d14e2d |
A383850 | Fixed points of A383848 and A383849. | [
"0",
"1",
"3",
"7",
"10",
"15",
"31",
"63",
"127",
"153",
"170",
"204",
"255",
"292",
"365",
"438",
"511",
"1023",
"2047",
"2275",
"2405",
"2470",
"2665",
"2730",
"2860",
"3185",
"3250",
"3380",
"3640",
"4095",
"8191",
"16383",
"32767",
"34695",
"34952",
"35723",
"36237",
"36494",
"37779",
"38293",
"38550",
"39321",
"39578",
"40092",
"41891",
"42405",
"42662",
"43433",
"43690"
]
| [
"nonn",
"base"
]
| 7 | 1 | 3 | [
"A000225",
"A383848",
"A383849",
"A383850"
]
| null | Paolo Xausa, May 13 2025 | 2025-05-14T14:09:22 | oeisdata/seq/A383/A383850.seq | c688f7fa5513c6da8e6c76e1045b26c6 |
A383851 | Decimal expansion of exp(8*G/Pi)*((1 - exp(-Pi/2))/(1 + exp(-Pi/2)))^2, where G is Catalan's constant (A006752). | [
"4",
"4",
"3",
"1",
"2",
"0",
"1",
"3",
"0",
"7",
"1",
"9",
"4",
"1",
"9",
"9",
"1",
"9",
"7",
"0",
"8",
"2",
"3",
"6",
"7",
"7",
"2",
"8",
"3",
"5",
"5",
"2",
"8",
"7",
"2",
"9",
"3",
"2",
"8",
"3",
"8",
"0",
"1",
"5",
"2",
"8",
"1",
"0",
"1",
"2",
"2",
"7",
"4",
"7",
"3",
"5",
"6",
"3",
"2",
"0",
"9",
"2",
"1",
"4",
"3",
"8",
"9",
"6",
"8",
"0",
"7",
"5",
"8",
"5",
"8",
"7",
"0",
"0",
"3",
"6",
"5",
"3",
"8",
"3",
"2",
"5",
"6",
"4",
"2",
"0"
]
| [
"nonn",
"cons",
"easy"
]
| 11 | 1 | 1 | [
"A006752",
"A049006",
"A377753",
"A383851"
]
| null | Paolo Xausa, May 13 2025 | 2025-05-14T14:09:34 | oeisdata/seq/A383/A383851.seq | 40d593a5843c5f63678531269af8d96c |
A383852 | Decimal expansion of the volume of an elongated triangular pyramid with unit edge. | [
"5",
"5",
"0",
"8",
"6",
"3",
"8",
"3",
"2",
"0",
"8",
"9",
"9",
"7",
"7",
"2",
"4",
"4",
"1",
"1",
"5",
"3",
"3",
"5",
"6",
"4",
"5",
"7",
"2",
"7",
"2",
"7",
"6",
"2",
"6",
"4",
"9",
"4",
"9",
"8",
"4",
"0",
"6",
"3",
"6",
"4",
"0",
"0",
"6",
"7",
"4",
"1",
"6",
"3",
"1",
"1",
"2",
"0",
"0",
"8",
"3",
"8",
"9",
"6",
"9",
"5",
"5",
"4",
"4",
"2",
"9",
"4",
"0",
"9",
"9",
"0",
"4",
"2",
"2",
"6",
"2",
"5",
"0",
"7",
"8",
"1",
"8",
"8",
"4",
"1"
]
| [
"nonn",
"cons",
"easy"
]
| 11 | 0 | 1 | [
"A002193",
"A010482",
"A165663",
"A383852"
]
| null | Paolo Xausa, May 19 2025 | 2025-05-22T09:54:33 | oeisdata/seq/A383/A383852.seq | dc84142e8a8b4404637b5ace03a49d5b |
A383853 | a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(4*n). | [
"1",
"1",
"260",
"556032",
"4641176128",
"106519579045760",
"5472276566891956224",
"549375993583284180705280",
"97867116732573493470161420288",
"28783909470167571938915053763592192",
"13216052972619446942074113385580542689280",
"9058922175695195359062480694771506779050213376"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A209289",
"A298851",
"A345876",
"A383853"
]
| null | Vaclav Kotesovec, May 12 2025 | 2025-05-13T00:57:57 | oeisdata/seq/A383/A383853.seq | fce9b7b3ec0bd04435b4bcab9925e9de |
A383854 | a(n) = 4*n^3 + 5*n - 1. | [
"8",
"41",
"122",
"275",
"524",
"893",
"1406",
"2087",
"2960",
"4049",
"5378",
"6971",
"8852",
"11045",
"13574",
"16463",
"19736",
"23417",
"27530",
"32099",
"37148",
"42701",
"48782",
"55415",
"62624",
"70433",
"78866",
"87947",
"97700",
"108149",
"119318",
"131231",
"143912",
"157385",
"171674",
"186803",
"202796",
"219677"
]
| [
"nonn",
"easy",
"changed"
]
| 30 | 1 | 1 | [
"A005893",
"A014106",
"A383854"
]
| null | Ed Pegg Jr, May 12 2025 | 2025-06-30T09:57:33 | oeisdata/seq/A383/A383854.seq | 7f573f6bac814a4855e87c836ebbae29 |
A383855 | The n-th term of the sequence is k after every k*(k+1)/2 occurrences of 1, with multiple values following a 1 listed in order. | [
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"2",
"1",
"4",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"2",
"5",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"4",
"1",
"2",
"6",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"2",
"1",
"7",
"1",
"1",
"2",
"3",
"4",
"5",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"3",
"8",
"1",
"1",
"1",
"2",
"1",
"4",
"1",
"1",
"2",
"3",
"6",
"1",
"1",
"1",
"2",
"5",
"9",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"4",
"1",
"2",
"1",
"1",
"1",
"2",
"3",
"1",
"10"
]
| [
"nonn"
]
| 16 | 1 | 4 | [
"A245254",
"A383855",
"A383899"
]
| null | Jwalin Bhatt, May 12 2025 | 2025-05-24T16:21:15 | oeisdata/seq/A383/A383855.seq | 5e56a6373bcae45f452c7237b14a6fd6 |
A383856 | Dimension in which a random vector of length n has the highest probability to fall into a single hypercube with side length of 10. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"4"
]
| [
"nonn",
"more",
"hard"
]
| 27 | 1 | 9 | null | null | Ruediger Jehn, May 12 2025 | 2025-06-16T18:30:38 | oeisdata/seq/A383/A383856.seq | 2b62b9f3c3246abdb6b54f0dae499b80 |
A383857 | Number of permutations of [n] such that precisely one rising or falling succession occurs, but without either n(n-1) or (n-1)n. | [
"0",
"0",
"2",
"8",
"34",
"196",
"1366",
"10928",
"98330",
"983036",
"10811134",
"129714184",
"1686103522",
"23603603540",
"354033474374",
"5664286296416",
"96289603698346",
"1733166940314028",
"32929480177913230",
"658578501071986616",
"13829959293448920434",
"304255691156335505924"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 3 | [
"A000130",
"A001100",
"A002464",
"A086852",
"A086856",
"A383857"
]
| null | Wolfdieter Lang, May 19 2025 | 2025-05-24T21:48:41 | oeisdata/seq/A383/A383857.seq | e3f72496fa34746918411fb6d39e4f89 |
A383858 | Irregular triangle read by rows: T(n,k) (n >= 4, 4 <= k <= A384502(n)) is the smallest n-digit number m with k distinct prime factors, such that these factors can be divided into two subsets of at least two elements each, both summing to the same value. If no such number exists, T(n,k) = -1. | [
"2145",
"2310",
"10725",
"10374",
"101065",
"100050",
"255255",
"510510",
"1005993",
"1000350",
"1036035",
"1009470",
"10006081",
"10000130",
"10012065",
"10004610",
"100010225",
"100001300",
"100001195",
"100009910",
"111546435",
"223092870",
"1000083889",
"1000008758",
"1000001751",
"1000005270",
"1002569295",
"1001110110"
]
| [
"sign",
"base",
"tabf",
"more"
]
| 53 | 4 | 1 | [
"A001221",
"A365795",
"A382469",
"A383677",
"A383725",
"A383726",
"A383728",
"A383729",
"A383858",
"A384502"
]
| null | Jean-Marc Rebert, May 12 2025 | 2025-06-24T16:18:53 | oeisdata/seq/A383/A383858.seq | b876613d9f975d69daa9188b319a815a |
A383859 | Central angle of the solution of the Tammes problem for 7 points on the sphere (in radians). | [
"1",
"3",
"5",
"9",
"0",
"7",
"9",
"8",
"9",
"7",
"6",
"3",
"2",
"6",
"6",
"0",
"1",
"4",
"1",
"8",
"8",
"5",
"0",
"0",
"2",
"8",
"8",
"1",
"6",
"4",
"7",
"3",
"3",
"2",
"7",
"5",
"3",
"7",
"8",
"3",
"0",
"2",
"1",
"4",
"5",
"9",
"8",
"6",
"1",
"2",
"8",
"2",
"4",
"9",
"1",
"3",
"2",
"6",
"2",
"8",
"0",
"7",
"8",
"3",
"7",
"1",
"5",
"9",
"7",
"3",
"9",
"8",
"1",
"6",
"5",
"8",
"7",
"6",
"9",
"7",
"2",
"4",
"2",
"6"
]
| [
"nonn",
"cons"
]
| 9 | 1 | 2 | [
"A019669",
"A019819",
"A105199",
"A137914",
"A217695",
"A340918",
"A381756",
"A383859",
"A383860",
"A383861"
]
| null | R. J. Mathar, May 12 2025 | 2025-05-19T15:47:00 | oeisdata/seq/A383/A383859.seq | 12e3142bc922f50fa73ffb2c91598e7e |
A383860 | Central angle of the solution of the Tammes problem for 14 points on the sphere (in radians). | [
"9",
"7",
"1",
"6",
"3",
"4",
"7",
"4",
"2",
"8",
"8",
"6",
"2",
"2",
"4",
"0",
"7",
"5",
"9",
"4",
"1",
"6",
"9",
"4",
"9",
"4",
"7",
"6",
"2",
"8",
"5",
"4",
"1",
"1",
"3",
"8",
"1",
"7",
"9",
"0",
"1",
"0",
"6",
"8",
"2",
"7",
"6",
"8",
"4",
"7",
"8",
"2",
"0",
"7",
"0",
"2",
"6",
"8",
"0",
"3",
"3",
"4",
"8",
"1",
"3",
"5",
"4",
"5",
"5",
"6",
"5",
"0",
"7",
"3",
"5",
"4",
"4",
"0",
"3",
"2",
"9",
"4",
"6",
"3",
"9",
"9",
"5",
"3",
"9",
"9",
"4"
]
| [
"nonn",
"cons"
]
| 8 | 0 | 1 | [
"A019669",
"A105199",
"A137914",
"A217695",
"A340918",
"A381756",
"A383859",
"A383860",
"A383861"
]
| null | R. J. Mathar, May 12 2025 | 2025-05-19T15:46:41 | oeisdata/seq/A383/A383860.seq | c3e9e0e79e41278f57d9266c13e2aa0c |
A383861 | Central angle of the solution of the Tammes problem for 24 points on the sphere (in radians). | [
"7",
"6",
"2",
"5",
"4",
"7",
"7",
"3",
"8",
"7",
"5",
"0",
"9",
"8",
"2",
"5",
"5",
"6",
"7",
"4",
"3",
"1",
"0",
"6",
"0",
"9",
"2",
"1",
"1",
"4",
"8",
"8",
"2",
"8",
"1",
"8",
"0",
"6",
"9",
"1",
"3",
"9",
"1",
"6",
"3",
"6",
"8",
"6",
"5",
"5",
"2",
"2",
"9",
"4",
"0",
"5",
"6",
"6",
"1",
"4",
"0",
"6",
"6",
"5",
"5",
"5",
"8",
"6",
"3",
"8",
"1",
"8",
"5",
"9",
"4",
"2",
"4",
"3",
"1",
"2",
"9",
"4",
"1",
"8",
"0",
"2",
"4",
"4",
"8",
"6",
"0",
"4",
"5",
"9",
"2",
"2",
"9",
"6",
"4",
"9",
"5",
"7",
"7",
"9",
"3",
"5",
"8",
"9",
"9",
"8",
"0",
"6",
"4",
"2"
]
| [
"nonn",
"cons"
]
| 8 | 0 | 1 | [
"A019669",
"A058265",
"A105199",
"A137914",
"A217695",
"A340918",
"A381756",
"A383859",
"A383860",
"A383861"
]
| null | R. J. Mathar, May 12 2025 | 2025-05-19T15:46:20 | oeisdata/seq/A383/A383861.seq | d23343792f851c6ebe27ed0f0ce8fc7b |
A383862 | a(n) = [x^n] Product_{k=0..n} 1/(1 - k*x)^3. | [
"1",
"3",
"48",
"1386",
"58278",
"3225915",
"221726711",
"18216234288",
"1741626159966",
"189977753488050",
"23285057201978520",
"3168272346322892094",
"473878954663846060735",
"77281168674525142984020",
"13647787698908399220563400",
"2594721838238358445753776000",
"528401900314147344955336365822"
]
| [
"nonn"
]
| 52 | 0 | 2 | [
"A007820",
"A350376",
"A383862",
"A384012",
"A384022",
"A384060"
]
| null | Seiichi Manyama, May 17 2025 | 2025-05-19T04:56:26 | oeisdata/seq/A383/A383862.seq | e9dcfa3126152142dd8a9bfec7dbee22 |
A383863 | The number of divisors d of n having the property that for every prime p dividing n the p-adic valuation of d is either 0 or a unitary divisor of the p-adic valuation of n. | [
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"3",
"3",
"4",
"2",
"6",
"2",
"4",
"4",
"3",
"2",
"6",
"2",
"6",
"4",
"4",
"2",
"6",
"3",
"4",
"3",
"6",
"2",
"8",
"2",
"3",
"4",
"4",
"4",
"9",
"2",
"4",
"4",
"6",
"2",
"8",
"2",
"6",
"6",
"4",
"2",
"6",
"3",
"6",
"4",
"6",
"2",
"6",
"4",
"6",
"4",
"4",
"2",
"12",
"2",
"4",
"6",
"5",
"4",
"8",
"2",
"6",
"4",
"8",
"2",
"9",
"2",
"4",
"6",
"6",
"4",
"8",
"2",
"6",
"3",
"4",
"2",
"12",
"4",
"4",
"4"
]
| [
"nonn",
"easy",
"mult"
]
| 10 | 1 | 2 | [
"A001221",
"A034444",
"A049419",
"A049599",
"A073184",
"A209061",
"A278908",
"A322791",
"A361255",
"A383863",
"A383864",
"A383865",
"A383867"
]
| null | Amiram Eldar, May 12 2025 | 2025-05-16T18:19:44 | oeisdata/seq/A383/A383863.seq | c2e9bfbc7ad075f4ae69e1546ca1e6a8 |
A383864 | The sum of divisors d of n having the property that for every prime p dividing n the p-adic valuation of d is either 0 or a unitary divisor of the p-adic valuation of n. | [
"1",
"3",
"4",
"7",
"6",
"12",
"8",
"11",
"13",
"18",
"12",
"28",
"14",
"24",
"24",
"19",
"18",
"39",
"20",
"42",
"32",
"36",
"24",
"44",
"31",
"42",
"31",
"56",
"30",
"72",
"32",
"35",
"48",
"54",
"48",
"91",
"38",
"60",
"56",
"66",
"42",
"96",
"44",
"84",
"78",
"72",
"48",
"76",
"57",
"93",
"72",
"98",
"54",
"93",
"72",
"88",
"80",
"90",
"60",
"168",
"62",
"96",
"104",
"79",
"84",
"144"
]
| [
"nonn",
"easy",
"mult"
]
| 11 | 1 | 2 | [
"A051377",
"A209061",
"A322791",
"A322857",
"A361255",
"A383863",
"A383864",
"A383866"
]
| null | Amiram Eldar, May 12 2025 | 2025-05-17T08:15:53 | oeisdata/seq/A383/A383864.seq | 1c83b368e28cc6fb4494da9c8f126955 |
A383865 | The number of divisors d of n having the property that for every prime p dividing n the p-adic valuation of d is either 0 or an infinitary divisor of the p-adic valuation of n. | [
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"3",
"3",
"4",
"2",
"6",
"2",
"4",
"4",
"3",
"2",
"6",
"2",
"6",
"4",
"4",
"2",
"6",
"3",
"4",
"3",
"6",
"2",
"8",
"2",
"3",
"4",
"4",
"4",
"9",
"2",
"4",
"4",
"6",
"2",
"8",
"2",
"6",
"6",
"4",
"2",
"6",
"3",
"6",
"4",
"6",
"2",
"6",
"4",
"6",
"4",
"4",
"2",
"12",
"2",
"4",
"6",
"5",
"4",
"8",
"2",
"6",
"4",
"8",
"2",
"9",
"2",
"4",
"6",
"6",
"4",
"8",
"2",
"6",
"3",
"4",
"2",
"12",
"4",
"4",
"4"
]
| [
"nonn",
"easy",
"mult"
]
| 7 | 1 | 2 | [
"A036537",
"A037445",
"A049419",
"A049599",
"A307848",
"A322791",
"A383760",
"A383863",
"A383865",
"A383866"
]
| null | Amiram Eldar, May 12 2025 | 2025-05-16T18:23:45 | oeisdata/seq/A383/A383865.seq | 3649dbcd55064df42383b5976c6ce2e9 |
A383866 | The sum of divisors d of n having the property that for every prime p dividing n the p-adic valuation of d is either 0 or an infinitary divisor of the p-adic valuation of n. | [
"1",
"3",
"4",
"7",
"6",
"12",
"8",
"11",
"13",
"18",
"12",
"28",
"14",
"24",
"24",
"19",
"18",
"39",
"20",
"42",
"32",
"36",
"24",
"44",
"31",
"42",
"31",
"56",
"30",
"72",
"32",
"35",
"48",
"54",
"48",
"91",
"38",
"60",
"56",
"66",
"42",
"96",
"44",
"84",
"78",
"72",
"48",
"76",
"57",
"93",
"72",
"98",
"54",
"93",
"72",
"88",
"80",
"90",
"60",
"168",
"62",
"96",
"104",
"79",
"84",
"144"
]
| [
"nonn",
"easy",
"mult"
]
| 12 | 1 | 2 | [
"A036537",
"A051377",
"A051378",
"A077609",
"A322791",
"A361175",
"A383760",
"A383864",
"A383865",
"A383866"
]
| null | Amiram Eldar, May 13 2025 | 2025-05-17T08:15:48 | oeisdata/seq/A383/A383866.seq | 49a914de0b4774023588262e6624b7a9 |
A383867 | The sum of divisors d of n having the property that for every prime p dividing n the p-adic valuation of d is either 0 or a squarefree divisor of the p-adic valuation of n. | [
"1",
"3",
"4",
"7",
"6",
"12",
"8",
"11",
"13",
"18",
"12",
"28",
"14",
"24",
"24",
"7",
"18",
"39",
"20",
"42",
"32",
"36",
"24",
"44",
"31",
"42",
"31",
"56",
"30",
"72",
"32",
"35",
"48",
"54",
"48",
"91",
"38",
"60",
"56",
"66",
"42",
"96",
"44",
"84",
"78",
"72",
"48",
"28",
"57",
"93",
"72",
"98",
"54",
"93",
"72",
"88",
"80",
"90",
"60",
"168",
"62",
"96",
"104",
"79",
"84",
"144",
"68"
]
| [
"nonn",
"easy",
"mult"
]
| 11 | 1 | 2 | [
"A051378",
"A209061",
"A322791",
"A361174",
"A383761",
"A383863",
"A383867"
]
| null | Amiram Eldar, May 13 2025 | 2025-05-17T08:15:25 | oeisdata/seq/A383/A383867.seq | 9c85553856bd8938d661f0aa6219e6d3 |
A383868 | a(n) = 2^(n-3)*(3*binomial(n,4) + 4*binomial(n,2) + 8). | [
"1",
"2",
"6",
"20",
"70",
"252",
"904",
"3152",
"10560",
"33920",
"104704",
"311808",
"899584",
"2524160",
"6912000",
"18526208",
"48726016",
"126025728",
"321126400",
"807403520",
"2005794816",
"4929093632",
"11994136576",
"28924968960",
"69185044480",
"164240556032",
"387201368064",
"907009851392",
"2112083722240"
]
| [
"nonn",
"easy"
]
| 10 | 0 | 2 | [
"A383778",
"A383868"
]
| null | Enrique Navarrete, May 12 2025 | 2025-05-18T18:40:12 | oeisdata/seq/A383/A383868.seq | 4206c05a111409f794c27923aca0f715 |
A383869 | a(n) = [x^n] 1/Product_{k=0..n} (1 - (n+k)*x). | [
"1",
"3",
"55",
"1890",
"95781",
"6427575",
"537306484",
"53791898160",
"6275077781973",
"835898091070185",
"125195263380478655",
"20825548503275385870",
"3809430011164368694260",
"759987002381075483922180",
"164221938436980055710082200",
"38209754165858724861944820000",
"9524153723280871205135022364485"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A007820",
"A129506",
"A143395",
"A383869"
]
| null | Seiichi Manyama, May 13 2025 | 2025-05-17T04:20:39 | oeisdata/seq/A383/A383869.seq | e0f02b7ce1d96eb92d9dbda757dbf224 |
A383870 | Number of compositions of n such that none of the smallest parts are adjacent. | [
"1",
"1",
"1",
"3",
"4",
"9",
"15",
"29",
"53",
"98",
"180",
"336",
"618",
"1142",
"2110",
"3899",
"7197",
"13283",
"24509",
"45218",
"83396",
"153769",
"283463",
"522449",
"962732",
"1773742",
"3267417",
"6018030",
"11082693",
"20407174",
"37572633",
"69169726",
"127326924",
"234362474",
"431343281",
"793831500",
"1460854117"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 4 | [
"A003242",
"A007318",
"A011782",
"A074909",
"A105039",
"A238342",
"A383870"
]
| null | John Tyler Rascoe, May 13 2025 | 2025-05-14T10:31:55 | oeisdata/seq/A383/A383870.seq | b58aebb9ba79a285e146c5805d8cdd94 |
A383871 | Number of labeled 3-nilpotent semigroups of order n | [
"0",
"0",
"6",
"180",
"11720",
"3089250",
"5944080072",
"147348275209800",
"38430603831264883632",
"90116197775746464859791750",
"2118031078806486819496589635743440",
"966490887282837500134221233339527160717340",
"17165261053166610940029331024343115375665769316911576",
"6444206974822296283920298148689544172139277283018112679406098010"
]
| [
"nonn"
]
| 12 | 1 | 3 | [
"A023814",
"A023815",
"A383871",
"A383885",
"A383886"
]
| null | Elijah Beregovsky, May 13 2025 | 2025-05-14T01:15:20 | oeisdata/seq/A383/A383871.seq | 1bf49a1f16b8a0e4032c46b72fc038a4 |
A383872 | Nonprime numbers whose sum of proper divisors is a power of 4. | [
"9",
"12",
"26",
"56",
"76",
"122",
"332",
"992",
"2042",
"3344",
"4336",
"8186",
"16256",
"32762",
"227744",
"266176",
"269072",
"299576",
"856544",
"2097146",
"5385812",
"8388602",
"16580864",
"17895664",
"19173944",
"33554426",
"61008020",
"67100672",
"201931760",
"1074789376",
"1108378592",
"17179738112",
"62472251540",
"68700578816"
]
| [
"nonn"
]
| 43 | 1 | 1 | [
"A001065",
"A048699",
"A135535",
"A279731",
"A383872"
]
| null | Hans Ulrich Keller, May 13 2025 | 2025-05-20T00:27:51 | oeisdata/seq/A383/A383872.seq | a949bba53eb8c50ad4fce749b8ab6d3e |
A383873 | a(n) = 3*a(n-1) - 2*a(n-2) + 5*a(n-3) starting with 1, 2, 3. | [
"1",
"2",
"3",
"10",
"34",
"97",
"273",
"795",
"2324",
"6747",
"19568",
"56830",
"165089",
"479447",
"1392313",
"4043490",
"11743079",
"34103822",
"99042758",
"287636025",
"835341669",
"2425966747",
"7045397028",
"20460965935",
"59421937484",
"172570865722",
"501173551873",
"1455488611595",
"4226973059649"
]
| [
"nonn",
"easy"
]
| 86 | 0 | 2 | null | null | Raul Prisacariu, May 18 2025 | 2025-05-21T01:22:29 | oeisdata/seq/A383/A383873.seq | 9a8952647f1d7bed501255f4b5732ff8 |
A383874 | a(n) = (3*n+1)!*(3*n)!/((2*n)!*((n+1)!)^2). | [
"1",
"18",
"4200",
"3175200",
"5137292160",
"14544244915200",
"64008493310361600",
"405192226643043840000",
"3493057136053143859200000",
"39378260464472988708249600000",
"562659674639968187756457984000000",
"9940535265182157971578474463232000000",
"212816707229761791940688046273331200000000"
]
| [
"nonn"
]
| 124 | 0 | 2 | [
"A064352",
"A166149",
"A166384",
"A166494",
"A166750",
"A166771",
"A271049",
"A383874"
]
| null | Karol A. Penson, May 22 2025 | 2025-05-26T11:27:43 | oeisdata/seq/A383/A383874.seq | 710a49806e224d2e46afd285ff13752c |
A383875 | Number of pairs in the Bruhat order of type A_n. | [
"1",
"3",
"19",
"213",
"3781",
"98407",
"3550919"
]
| [
"nonn",
"more",
"changed"
]
| 51 | 0 | 2 | [
"A000142",
"A002538",
"A005130",
"A383875",
"A384061",
"A384062"
]
| null | Dmitry I. Ignatov, May 18 2025 | 2025-07-02T15:50:14 | oeisdata/seq/A383/A383875.seq | d6eb3e155757fe5081f66aecbdcd1a79 |
A383876 | a(0) = 0, a(1) = 1. Let n be greatest index such that a(0),...a(n) are already known. If a(n) is not a record term, a(n+1) = number of k < n such that a(k) = a(n). If a(n) is a record term a(n+1) = a(r) where r is the greatest record < a(n). | [
"0",
"1",
"0",
"1",
"1",
"2",
"1",
"3",
"0",
"2",
"1",
"4",
"1",
"5",
"1",
"6",
"2",
"2",
"3",
"1",
"7",
"1",
"8",
"3",
"2",
"4",
"1",
"9",
"0",
"3",
"3",
"4",
"2",
"5",
"1",
"10",
"2",
"6",
"1",
"11",
"1",
"12",
"4",
"3",
"5",
"2",
"7",
"1",
"13",
"1",
"14",
"5",
"3",
"6",
"2",
"8",
"1",
"15",
"1",
"16",
"6",
"3",
"7",
"2",
"9",
"1",
"17",
"2",
"10",
"1",
"18",
"2",
"11",
"1",
"19",
"3",
"8",
"2",
"12",
"1",
"20",
"1",
"21"
]
| [
"nonn",
"easy"
]
| 15 | 0 | 6 | [
"A001477",
"A025480",
"A181391",
"A346175",
"A383876"
]
| null | David James Sycamore, May 13 2025 | 2025-05-19T23:03:22 | oeisdata/seq/A383/A383876.seq | 90b686b4dd19d50df5202b5a1105724e |
A383877 | a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^3, where 0 < x < y < z < w has exactly n integer solutions, or 0 if there is no such k. | [
"14",
"13",
"55",
"26",
"52",
"63",
"70",
"66",
"56",
"104",
"102",
"143",
"161",
"91",
"117",
"112",
"78",
"236",
"180",
"217",
"198",
"192",
"140",
"292",
"216",
"259",
"156",
"196",
"344",
"168",
"210",
"264",
"325",
"252",
"406",
"360",
"380",
"402",
"315",
"338",
"234",
"308",
"351",
"182",
"396",
"408",
"399",
"432",
"441",
"312",
"474",
"636",
"513",
"273",
"336",
"476",
"618",
"666"
]
| [
"nonn"
]
| 38 | 1 | 1 | [
"A377444",
"A383877",
"A384439"
]
| null | Zhining Yang, May 13 2025 | 2025-06-14T17:58:48 | oeisdata/seq/A383/A383877.seq | 6b9b00d677eb7d83b8f99c0ffedc8c7f |
A383878 | Number of permutations of [n] with distinct cycle lengths whose GCD is 1. | [
"0",
"1",
"0",
"3",
"8",
"50",
"264",
"2394",
"15840",
"158976",
"1490400",
"20124720",
"181543680",
"3213905760",
"36459964800",
"602127540000",
"9045463311360",
"187660890063360",
"2596164765465600",
"64849189355274240",
"1037566851245568000",
"24684232291242854400",
"498833466644833689600"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A079128",
"A382781",
"A383878"
]
| null | Alois P. Heinz, May 13 2025 | 2025-05-13T11:16:31 | oeisdata/seq/A383/A383878.seq | 0987c9a93e5724977e30dcf9c395dc2f |
A383879 | a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^n, where 0 < x < y < z < w has exactly n integer solutions. | [
"100",
"42",
"55",
"34",
"74"
]
| [
"nonn",
"hard",
"more"
]
| 11 | 1 | 1 | [
"A383689",
"A383879"
]
| null | Zhining Yang, May 13 2025 | 2025-05-19T15:30:29 | oeisdata/seq/A383/A383879.seq | 00593eacd4f7b4fc27bc65976f5e60e5 |
A383880 | a(n) = [x^n] 1/Product_{k=0..n-1} (1 - k*x)^2. | [
"1",
"0",
"3",
"72",
"2307",
"95060",
"4817990",
"290523576",
"20333487251",
"1621036680120",
"145057745669850",
"14399349523416000",
"1570425994090538574",
"186674663305762642296",
"24021930409036829669036",
"3327140929951823209016400",
"493515678917684006649451651",
"78054583374364036172432641200"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A342111",
"A350376",
"A383880",
"A383883"
]
| null | Seiichi Manyama, May 13 2025 | 2025-05-14T04:08:42 | oeisdata/seq/A383/A383880.seq | 36eb47f4c3e2bbad25a5d8358a508db5 |
A383881 | a(n) = [x^n] Product_{k=1..3*n} 1/(1 - k*x). | [
"1",
"6",
"266",
"22275",
"2757118",
"452329200",
"92484925445",
"22653141490980",
"6466506598695390",
"2108114165258886708",
"772778072287000494520",
"314641228029527540596455",
"140880584836935832288402135",
"68799366730032076856334789900",
"36392216443342587869022660451080",
"20728132932716479897744043460870000"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A007820",
"A217913",
"A348084",
"A383881",
"A383882"
]
| null | Vaclav Kotesovec, May 13 2025 | 2025-05-21T11:14:40 | oeisdata/seq/A383/A383881.seq | a0c405ec124713f11c1df4fb23a529b8 |
A383882 | a(n) = [x^n] Product_{k=1..4*n} 1/(1 - k*x). | [
"1",
"10",
"750",
"106470",
"22350954",
"6220194750",
"2157580085700",
"896587036640680",
"434225240080346858",
"240175986308550372366",
"149377949042637543000150",
"103192471874508023383125750",
"78394850841083734162487127720",
"64957213308036504429927388238088",
"58298851680969051596827194829579744"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A007820",
"A187646",
"A217913",
"A348084",
"A383881",
"A383882",
"A384129",
"A384130"
]
| null | Vaclav Kotesovec, May 13 2025 | 2025-05-23T06:15:52 | oeisdata/seq/A383/A383882.seq | c23b80ac7996680a85f78d6c3e638e8f |
A383883 | a(n) = [x^n] 1/((1 - n*x) * Product_{k=0..n-1} (1 - k*x)^2). | [
"1",
"1",
"11",
"222",
"6627",
"262570",
"12978758",
"769079444",
"53138842515",
"4194648739710",
"372421403333850",
"36733739199892020",
"3985122473105099406",
"471598870326072262644",
"60456151456891375730860",
"8345905345383943433713800",
"1234395864446065862689721475",
"194738649118647202909304657910"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A187235",
"A287532",
"A350376",
"A383880",
"A383883"
]
| null | Seiichi Manyama, May 13 2025 | 2025-05-14T09:08:19 | oeisdata/seq/A383/A383883.seq | 511ee0cc3c0fc395dc2bfde9de744105 |
A383885 | Number of nonisomorphic 3-nilpotent semigroups of order n | [
"0",
"0",
"1",
"9",
"118",
"4671",
"1199989",
"3661522792",
"105931872028455",
"24834563582168716305",
"53061406576514239124327751",
"2017720196187069550262596208732035",
"2756576827989210680367439732667802738773384",
"73919858836708511517426763179873538289329852786253510",
"29599937964452484359589007277447538854227891149791717673581110642"
]
| [
"nonn"
]
| 12 | 1 | 4 | [
"A023814",
"A027851",
"A383871",
"A383885",
"A383886"
]
| null | Elijah Beregovsky, May 13 2025 | 2025-05-14T01:16:29 | oeisdata/seq/A383/A383885.seq | cf42135994bdf126d460223dbccc4436 |
A383886 | Number of 3-nilpotent semigroups, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). | [
"0",
"0",
"1",
"8",
"84",
"2660",
"609797",
"1831687022",
"52966239062973",
"12417282095522918811",
"26530703289252298687053072",
"1008860098093547692911901804990610",
"1378288413994605341053354105969660808031163",
"36959929418354255758713676933402538920157765946956889",
"14799968982226242179794503639146983952853044950740907666303436922"
]
| [
"nonn"
]
| 7 | 1 | 4 | [
"A001423",
"A023814",
"A383871",
"A383885",
"A383886"
]
| null | Elijah Beregovsky, May 13 2025 | 2025-05-14T01:16:42 | oeisdata/seq/A383/A383886.seq | fd9f00cd910a4e455a365890fbafe2db |
A383887 | Smallest non-palindromic number that is congruent to its reverse mod n. | [
"10",
"13",
"10",
"15",
"16",
"13",
"18",
"19",
"10",
"1011",
"100",
"15",
"1017",
"1027",
"16",
"1025",
"1039",
"13",
"1048",
"1021",
"18",
"103",
"1026",
"19",
"1026",
"1017",
"14",
"1033",
"1013",
"1011",
"1068",
"1049",
"100",
"1039",
"1046",
"15",
"1000",
"1055",
"1017",
"1041",
"1066",
"1027",
"1048",
"105",
"16",
"1077",
"1032",
"1025",
"1014",
"1051",
"1039",
"1017",
"1103",
"17",
"106",
"1065"
]
| [
"nonn",
"base",
"easy"
]
| 98 | 1 | 1 | [
"A004086",
"A056965",
"A070837",
"A383887"
]
| null | Erick B. Wong, May 29 2025, at the suggestion of Lanny Wong | 2025-06-04T10:24:38 | oeisdata/seq/A383/A383887.seq | bca312a25682b784845856f773a419b8 |
A383889 | Record high points in A083533. | [
"1",
"2",
"4",
"6",
"10",
"12",
"16",
"18",
"20",
"22",
"24",
"26",
"28",
"32",
"36",
"40",
"44",
"50",
"60",
"64",
"72",
"74",
"76",
"78",
"80",
"90",
"96",
"108",
"112"
]
| [
"nonn",
"more"
]
| 20 | 1 | 2 | [
"A000010",
"A002202",
"A083533",
"A383889",
"A383890"
]
| null | Jud McCranie, May 13 2025 | 2025-05-22T09:53:23 | oeisdata/seq/A383/A383889.seq | 75167c169dc225f9ed0605d79410acea |
A383890 | Index of record gaps between totient numbers. | [
"1",
"2",
"7",
"30",
"85",
"257",
"1031",
"2493",
"3288",
"7604",
"13392",
"22663",
"26818",
"31377",
"110175",
"186971",
"400432",
"890621",
"1536566",
"17176199",
"27501485",
"102834105",
"173246634",
"182261294",
"214104745",
"268935021",
"1781734397",
"4010389565",
"6213586719"
]
| [
"nonn",
"more"
]
| 12 | 1 | 2 | [
"A000010",
"A002202",
"A083533",
"A383889",
"A383890"
]
| null | Jud McCranie, May 13 2025 | 2025-05-22T09:11:41 | oeisdata/seq/A383/A383890.seq | 32f23630b6362e1baa4c3c7dc15fcec8 |
A383891 | a(n) is the length of chunks of the prime number sequence such that each chunk’s sum of reciprocals is no less than 1/n, chunks being consecutive and of minimal length, for n>=2. | [
"1",
"1",
"2",
"3",
"5",
"8",
"13",
"22",
"36",
"60",
"100",
"168",
"284",
"482",
"819",
"1397",
"2389",
"4096",
"7044",
"12137",
"20956",
"36259"
]
| [
"nonn",
"more"
]
| 11 | 2 | 3 | [
"A000040",
"A383891"
]
| null | Xiaoliang Zhang, May 13 2025 | 2025-05-19T17:47:16 | oeisdata/seq/A383/A383891.seq | e41582cc263556aa8be53fe3d91daa8a |
A383892 | Expansion of 1/( ((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 * (1-5*x) ). | [
"1",
"25",
"355",
"3775",
"33502",
"262570",
"1880090",
"12574850",
"79778303",
"485441135",
"2856558005",
"16358449625",
"91615095204",
"503740623720",
"2727832278900",
"14584759018500",
"77152991893005",
"404503014170325",
"2104862289863575",
"10883633564375875",
"55976319375728506",
"286601257317512950"
]
| [
"nonn",
"easy"
]
| 18 | 0 | 2 | [
"A287532",
"A383842",
"A383892"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-28T18:39:57 | oeisdata/seq/A383/A383892.seq | 02883b9b1ac6a0c81f3dd82a442f0131 |
A383893 | Expansion of 1/( ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x))^2 * (1-6*x) ). | [
"1",
"36",
"721",
"10626",
"128758",
"1360128",
"12978758",
"114537348",
"950326391",
"7502910996",
"56878787231",
"416937779286",
"2971567050420",
"20682844799760",
"141092113563660",
"946112664225960",
"6251628891468765",
"40789040893547940",
"263235445374827965",
"1682802305881045290",
"10669738322822387746"
]
| [
"nonn",
"easy"
]
| 17 | 0 | 2 | [
"A287532",
"A383893"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-28T18:39:45 | oeisdata/seq/A383/A383893.seq | 39b8d654fd26b0852af050fdda7720fa |
A383894 | Number of arborescent partitions with exactly n parts. | [
"1",
"1",
"2",
"4",
"9",
"19",
"44",
"96",
"220",
"489",
"1115",
"2483",
"5646",
"12571",
"28343",
"63152",
"141621",
"314330",
"701327",
"1552149",
"3445128",
"7599990",
"16789039",
"36908077"
]
| [
"nonn",
"more"
]
| 15 | 1 | 3 | [
"A000081",
"A382440",
"A383894",
"A383895"
]
| null | Ludovic Schwob, May 14 2025 | 2025-05-28T01:08:42 | oeisdata/seq/A383/A383894.seq | b234fe4d49c3e0204780fc5afc62a7fe |
A383895 | Number of spiny partitions with exactly n parts. | [
"1",
"1",
"2",
"4",
"9",
"20",
"47",
"111",
"267",
"646",
"1582",
"3892",
"9636",
"23961",
"59871",
"150128",
"377738",
"953029",
"2410626",
"6111055",
"15524013",
"39508683",
"100719223",
"257150952",
"657454544",
"1683042629",
"4313582090",
"11067748352",
"28426813910",
"73082880708",
"188059428289",
"484330230117",
"1248338233493"
]
| [
"nonn",
"changed"
]
| 20 | 0 | 3 | [
"A382440",
"A383894",
"A383895"
]
| null | Ludovic Schwob, May 14 2025 | 2025-06-30T16:00:08 | oeisdata/seq/A383/A383895.seq | d190db8b7b89c38c3d386ef90f25242c |
A383896 | Echo numbers: positive integers k such that the largest prime factor of k-1 is a suffix of k. | [
"13",
"57",
"73",
"111",
"127",
"163",
"193",
"197",
"313",
"323",
"337",
"419",
"433",
"687",
"757",
"817",
"847",
"897",
"929",
"931",
"973",
"1037",
"1153",
"1177",
"1211",
"1641",
"2017",
"2311",
"2593",
"2623",
"2647",
"2913",
"3073",
"3137",
"3659",
"3661",
"3829",
"4031",
"4117",
"4213",
"4453",
"4483",
"4537",
"4673",
"4737",
"4971",
"5377",
"5741"
]
| [
"nonn",
"base"
]
| 39 | 1 | 1 | [
"A006530",
"A383296",
"A383896",
"A383927"
]
| null | Giorgos Kalogeropoulos, May 14 2025 | 2025-05-29T00:53:15 | oeisdata/seq/A383/A383896.seq | f25fd17e23315a3598feb2d58771bcc4 |
A383897 | Expansion of e.g.f. log(1 + x)/(1 - 2*x). | [
"0",
"1",
"3",
"20",
"154",
"1564",
"18648",
"261792",
"4183632",
"75345696",
"1506551040",
"33147751680",
"795506123520",
"20683638213120",
"579135642946560",
"17374156466688000",
"555971699259648000",
"18903058697617920000",
"680509757426817024000",
"25859377184592752640000",
"1034374965738609696768000"
]
| [
"nonn",
"easy"
]
| 49 | 0 | 3 | [
"A024167",
"A068102",
"A383897",
"A384199"
]
| null | Seiichi Manyama, May 22 2025 | 2025-05-29T00:52:08 | oeisdata/seq/A383/A383897.seq | d431f48970d7fb7b5fcec13d340b27c9 |
A383898 | a(n) is the smallest nonnegative integer k such that n + k and n*k are squares, or -1 if there is no such number. | [
"0",
"2",
"-1",
"0",
"20",
"-1",
"-1",
"8",
"0",
"90",
"-1",
"-1",
"4212",
"-1",
"-1",
"0",
"272",
"18",
"-1",
"5",
"-1",
"-1",
"-1",
"-1",
"0",
"650",
"-1",
"-1",
"142100",
"-1",
"-1",
"32",
"-1",
"-1",
"-1",
"0",
"1332",
"-1",
"-1",
"360",
"41984",
"-1",
"-1",
"-1",
"180",
"-1",
"-1",
"-1",
"0",
"50",
"-1",
"117",
"1755572",
"-1",
"-1",
"-1",
"-1",
"568458",
"-1",
"-1",
"53872730964"
]
| [
"sign"
]
| 37 | 1 | 2 | [
"A245226",
"A382209",
"A383734",
"A383898"
]
| null | Gonzalo Martínez, May 15 2025 | 2025-05-24T10:35:24 | oeisdata/seq/A383/A383898.seq | e12786c0b921756b164fb91466c1262d |
A383899 | A sequence constructed by greedily sampling the Yule-Simon distribution for parameter value 1, 1/(i*(i+1)) to minimize discrepancy. | [
"1",
"2",
"1",
"3",
"1",
"4",
"1",
"2",
"1",
"5",
"1",
"6",
"1",
"2",
"1",
"3",
"1",
"7",
"1",
"2",
"1",
"8",
"1",
"9",
"1",
"2",
"1",
"4",
"1",
"3",
"1",
"2",
"1",
"10",
"1",
"11",
"1",
"2",
"1",
"3",
"1",
"5",
"1",
"2",
"1",
"4",
"1",
"12",
"1",
"2",
"1",
"3",
"1",
"13",
"1",
"2",
"1",
"6",
"1",
"14",
"1",
"2",
"1",
"3",
"1",
"4",
"1",
"2",
"1",
"5",
"1",
"15",
"1",
"2",
"1",
"7",
"1",
"3",
"1",
"2",
"1",
"16",
"1",
"17"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A245254",
"A383855",
"A383899"
]
| null | Jwalin Bhatt, May 14 2025 | 2025-06-06T00:15:41 | oeisdata/seq/A383/A383899.seq | 95bd6b39ae249266328732193bf9b6d8 |
A383900 | Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of Product_{j=0..k} (1 + j*x)/(1 - j*x). | [
"1",
"1",
"0",
"1",
"2",
"0",
"1",
"6",
"2",
"0",
"1",
"12",
"18",
"2",
"0",
"1",
"20",
"72",
"42",
"2",
"0",
"1",
"30",
"200",
"312",
"90",
"2",
"0",
"1",
"42",
"450",
"1400",
"1152",
"186",
"2",
"0",
"1",
"56",
"882",
"4650",
"8000",
"3912",
"378",
"2",
"0",
"1",
"72",
"1568",
"12642",
"38250",
"40520",
"12672",
"762",
"2",
"0",
"1",
"90",
"2592",
"29792",
"142002",
"271770",
"190400",
"39912",
"1530",
"2",
"0"
]
| [
"nonn",
"tabl"
]
| 29 | 0 | 5 | [
"A000007",
"A040000",
"A068293",
"A350366",
"A383767",
"A383818",
"A383843",
"A383900",
"A383910",
"A383911"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-15T08:22:02 | oeisdata/seq/A383/A383900.seq | f5fa3f2341596ae5765162afa88544cd |
A383902 | Square table read by ascending antidiagonals where T(n,k) = binomial(k+2^n-2,k). | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"3",
"1",
"0",
"1",
"7",
"6",
"1",
"0",
"1",
"15",
"28",
"10",
"1",
"0",
"1",
"31",
"120",
"84",
"15",
"1",
"0",
"1",
"63",
"496",
"680",
"210",
"21",
"1",
"0",
"1",
"127",
"2016",
"5456",
"3060",
"462",
"28",
"1",
"0",
"1",
"255",
"8128",
"43680",
"46376",
"11628",
"924",
"36",
"1",
"0",
"1",
"511",
"32640",
"349504",
"720720",
"324632",
"38760",
"1716",
"45",
"1",
"0"
]
| [
"nonn",
"tabl"
]
| 18 | 0 | 8 | [
"A092056",
"A383902",
"A383905"
]
| null | Isaac R. Browne, May 15 2025 | 2025-05-26T17:48:56 | oeisdata/seq/A383/A383902.seq | 2f64b4d2dbc62693cd88324b05ab4c5b |
A383905 | Square table read by descending antidiagonals where T(n,k) = binomial(k+2^n-2,k). | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"3",
"1",
"0",
"1",
"6",
"7",
"1",
"0",
"1",
"10",
"28",
"15",
"1",
"0",
"1",
"15",
"84",
"120",
"31",
"1",
"0",
"1",
"21",
"210",
"680",
"496",
"63",
"1",
"0",
"1",
"28",
"462",
"3060",
"5456",
"2016",
"127",
"1",
"0",
"1",
"36",
"924",
"11628",
"46376",
"43680",
"8128",
"255",
"1",
"0",
"1",
"45",
"1716",
"38760",
"324632",
"720720",
"349504",
"32640",
"511",
"1"
]
| [
"nonn",
"tabl"
]
| 14 | 0 | 9 | [
"A137153",
"A383902",
"A383905"
]
| null | Isaac R. Browne, May 15 2025 | 2025-05-26T17:48:15 | oeisdata/seq/A383/A383905.seq | 4378c2cac24279b28a811434e5660f8f |
A383907 | Echo primes: primes p such that the greatest prime factor of p-1 is a suffix of p. | [
"13",
"73",
"127",
"163",
"193",
"197",
"313",
"337",
"419",
"433",
"757",
"929",
"1153",
"2017",
"2311",
"2593",
"2647",
"3137",
"3659",
"4483",
"4673",
"5741",
"6857",
"7057",
"12071",
"12097",
"13267",
"13313",
"13619",
"14407",
"15877",
"17191",
"18041",
"18433",
"18439",
"19273",
"19531",
"20353",
"21319",
"21961",
"22279",
"24103",
"24697",
"25411"
]
| [
"nonn",
"base"
]
| 16 | 1 | 1 | [
"A000040",
"A006530",
"A383896",
"A383907"
]
| null | Giorgos Kalogeropoulos, May 15 2025 | 2025-05-20T18:40:55 | oeisdata/seq/A383/A383907.seq | 2bd1c6e4cffe87ed89828632b5732001 |
A383908 | Number of generalized polyforms with n cells on the snub trihexagonal tiling. | [
"1",
"3",
"3",
"7",
"23",
"69",
"228",
"766",
"2642",
"9309",
"33382",
"120629",
"439752",
"1613135",
"5953061",
"22075011",
"82204128",
"307213215",
"1151820825",
"4330858682",
"16326297768",
"61690058385"
]
| [
"nonn",
"more",
"hard"
]
| 17 | 0 | 2 | [
"A000105",
"A000228",
"A000577",
"A197156",
"A197159",
"A197459",
"A197462",
"A197465",
"A309159",
"A343398",
"A343406",
"A343577",
"A344211",
"A344213",
"A383908"
]
| null | Peter Kagey, May 14 2025 | 2025-06-06T08:35:32 | oeisdata/seq/A383/A383908.seq | b6b95881b59ba0dbaadcb53dbfd53732 |
A383909 | In the base 4 expansion of n, map: 0 -> 20, 1 -> 21, 2 -> 30, 3 -> 31. | [
"8",
"9",
"12",
"13",
"152",
"153",
"156",
"157",
"200",
"201",
"204",
"205",
"216",
"217",
"220",
"221",
"2440",
"2441",
"2444",
"2445",
"2456",
"2457",
"2460",
"2461",
"2504",
"2505",
"2508",
"2509",
"2520",
"2521",
"2524",
"2525",
"3208",
"3209",
"3212",
"3213",
"3224",
"3225",
"3228",
"3229",
"3272",
"3273",
"3276",
"3277",
"3288",
"3289",
"3292",
"3293"
]
| [
"nonn",
"base",
"easy"
]
| 25 | 0 | 1 | [
"A014577",
"A383909"
]
| null | Darío Clavijo, May 14 2025 | 2025-05-22T09:34:45 | oeisdata/seq/A383/A383909.seq | e2fbcdccfa7f1885916952417b720034 |
A383910 | Expansion of Product_{k=0..3} (1 + k*x)/(1 - k*x). | [
"1",
"12",
"72",
"312",
"1152",
"3912",
"12672",
"39912",
"123552",
"378312",
"1150272",
"3481512",
"10505952",
"31640712",
"95167872",
"285995112",
"858968352",
"2578871112",
"7740545472",
"23229500712",
"69704230752",
"209144149512",
"627495363072",
"1882611918312",
"5648087413152",
"16944765555912",
"50835303300672"
]
| [
"nonn",
"easy"
]
| 18 | 0 | 2 | [
"A091344",
"A383900",
"A383910",
"A383912"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-15T07:10:35 | oeisdata/seq/A383/A383910.seq | 20ed8b2f76a976f8384758c8e9869300 |
A383911 | Expansion of Product_{k=0..4} (1 + k*x)/(1 - k*x). | [
"1",
"20",
"200",
"1400",
"8000",
"40520",
"190400",
"852200",
"3692000",
"15640520",
"65225600",
"268985000",
"1100372000",
"4475152520",
"18122340800",
"73156029800",
"294627068000",
"1184523016520",
"4756148096000",
"19078784066600",
"76477758500000",
"306398995072520",
"1227060052251200",
"4912632802375400",
"19663709744588000"
]
| [
"nonn",
"easy"
]
| 16 | 0 | 2 | [
"A383900",
"A383911",
"A383913"
]
| null | Seiichi Manyama, May 14 2025 | 2025-05-15T06:56:01 | oeisdata/seq/A383/A383911.seq | 3b68572fd3003b21e267447b50d12765 |
A383912 | Expansion of (1+x) * (1+2*x)/((1-x) * (1-2*x) * (1-3*x)). | [
"1",
"9",
"45",
"177",
"621",
"2049",
"6525",
"20337",
"62541",
"190689",
"578205",
"1746897",
"5265261",
"15844929",
"47633085",
"143095857",
"429680781",
"1289828769",
"3871059165",
"11616323217",
"34855261101",
"104578366209",
"313760264445",
"941331124977",
"2824094038221",
"8472483441249",
"25417852976925"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 2 | [
"A383818",
"A383910",
"A383912"
]
| null | Seiichi Manyama, May 15 2025 | 2025-05-15T06:57:52 | oeisdata/seq/A383/A383912.seq | 24e3ad0545f6f73765985800faa9c314 |
A383913 | Expansion of (1+x) * (1+2*x) * (1+3*x)/((1-x) * (1-2*x) * (1-3*x) * (1-4*x)). | [
"1",
"16",
"136",
"856",
"4576",
"22216",
"101536",
"446056",
"1907776",
"8009416",
"33187936",
"136233256",
"555438976",
"2253396616",
"9108754336",
"36721012456",
"147743018176",
"593550943816",
"2381944320736",
"9551006783656",
"38273731365376",
"153304069611016",
"613843773807136",
"2457257707146856"
]
| [
"nonn",
"easy"
]
| 10 | 0 | 2 | [
"A383818",
"A383911",
"A383913"
]
| null | Seiichi Manyama, May 15 2025 | 2025-05-15T07:01:00 | oeisdata/seq/A383/A383913.seq | 8e55c173fbf88b258c2a20cb8e4a8629 |
A383914 | Primes p such that 12*2^p + 1 is also prime. | [
"3",
"199",
"3187",
"44683",
"59971",
"213319",
"303091",
"916771"
]
| [
"nonn",
"more"
]
| 11 | 1 | 1 | [
"A002253",
"A175172",
"A322301",
"A322302",
"A383914"
]
| null | Vincenzo Librandi, May 17 2025 | 2025-05-21T01:39:16 | oeisdata/seq/A383/A383914.seq | 1ab2f5570d996ea3bb0bc9ab3ae60486 |
A383915 | Number of points enclosed by the unique circle that goes through the 8 points (-n, 0), (-n, 1), (0, n+1), (1, n+1), (n+1, 1), (n+1, 0), (1, -n), (0, -n). | [
"4",
"16",
"32",
"60",
"88",
"124",
"172",
"216",
"276",
"332",
"408",
"484",
"560",
"648",
"740",
"848",
"952",
"1060",
"1184",
"1304",
"1436",
"1576",
"1716",
"1876",
"2032",
"2188",
"2348",
"2536",
"2724",
"2912",
"3096",
"3300",
"3512",
"3720",
"3940",
"4160",
"4404",
"4644",
"4872",
"5140",
"5388",
"5664",
"5924",
"6180",
"6488",
"6772",
"7080",
"7368",
"7668",
"8000"
]
| [
"nonn"
]
| 31 | 1 | 1 | [
"A000328",
"A162431",
"A383915"
]
| null | Michel Marcus, May 15 2025 | 2025-05-22T20:57:13 | oeisdata/seq/A383/A383915.seq | 99093db1642a1e0237cb85868e4909bd |
A383916 | a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(3*n). | [
"1",
"1",
"68",
"22770",
"21143488",
"41904629550",
"151957171590144",
"910666718387157732",
"8390164064875701321728",
"112583179357513548960803670",
"2109812207969377622615440752640",
"53397692462483465346961668429307836",
"1775866125092261344436828225211633500160",
"75857512919848315654302238627976991244564300"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A032443",
"A209289",
"A345876",
"A383853",
"A383916",
"A383917"
]
| null | Vaclav Kotesovec, May 15 2025 | 2025-05-15T08:18:10 | oeisdata/seq/A383/A383916.seq | 566fe87dcaae4bdde120945586927b7a |
A383917 | a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(5*n). | [
"1",
"1",
"1028",
"14545530",
"1127435263168",
"309320354959336350",
"232325928732003715014144",
"403150958104730561230009068564",
"1432706082674749593552098155989352448",
"9528431104471630510834164178027409070527670",
"110580781643902847320855308323644986008860441968640"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A032443",
"A209289",
"A345876",
"A383853",
"A383916",
"A383917"
]
| null | Vaclav Kotesovec, May 15 2025 | 2025-05-15T08:18:06 | oeisdata/seq/A383/A383917.seq | 50ef888ca3069252e0460b060852b295 |
A383918 | Primes made up of 0's and five 1's only. | [
"101111",
"10011101",
"10101101",
"10110011",
"10111001",
"11000111",
"11100101",
"100100111",
"100111001",
"101001011",
"101100011",
"110010101",
"110101001",
"111000101",
"111001001",
"1000011011",
"1000110101",
"1001000111",
"1001001011",
"1001010011",
"1010000111",
"1010001101",
"1010010011",
"1010100011",
"1010110001"
]
| [
"nonn",
"base"
]
| 23 | 1 | 1 | [
"A020449",
"A038447",
"A157711",
"A383918"
]
| null | René-Louis Clerc, May 15 2025 | 2025-05-29T14:40:13 | oeisdata/seq/A383/A383918.seq | 3a1575c3b67320adec36bbab0033d3a8 |
A383919 | Primes made up of 0's and seven 1's only. | [
"11110111",
"11111101",
"101101111",
"101111011",
"110111011",
"111010111",
"1001110111",
"1010011111",
"1011110011",
"1100101111",
"1101010111",
"1101110011",
"1110011101",
"1110110011",
"1111100101",
"1111110001",
"10010110111",
"10011101011",
"10011110101",
"10100111101",
"10111001011",
"10111110001",
"11001011101"
]
| [
"nonn",
"base"
]
| 23 | 1 | 1 | [
"A020449",
"A038447",
"A062337",
"A157711",
"A383919"
]
| null | René-Louis Clerc, May 15 2025 | 2025-05-28T21:27:26 | oeisdata/seq/A383/A383919.seq | 6453cc32a0082b82b20877f4f5891ab4 |
A383920 | Smallest m such that sigma(m) >= n*m/2. | [
"1",
"2",
"6",
"24",
"120",
"1680",
"27720",
"720720",
"122522400",
"41902660800",
"130429015516800",
"3066842656354276800",
"1970992304700453905270400",
"168721307030313765796546413936000",
"1897544233056092162003806758651798777216000",
"8201519488959040182625924708238885435575055666675808000"
]
| [
"nonn"
]
| 22 | 2 | 2 | [
"A000203",
"A004394",
"A004490",
"A023199",
"A317681",
"A383920"
]
| null | Michel Marcus, May 15 2025 | 2025-05-22T11:45:55 | oeisdata/seq/A383/A383920.seq | 79ecb552a5cdf944aae67a234ab9a638 |
A383921 | Least integer k for which sigma(k - x) + sigma(k + x) >= n*k has at least one solution. | [
"1",
"2",
"6",
"24",
"91",
"841",
"13861",
"360361"
]
| [
"nonn",
"more"
]
| 19 | 2 | 2 | [
"A000203",
"A004394",
"A383758",
"A383920",
"A383921"
]
| null | Michel Marcus, May 15 2025 | 2025-05-22T09:39:19 | oeisdata/seq/A383/A383921.seq | d63fed80dba988d431f1733b83f73e63 |
A383922 | a(n) = A002104(n) + A002104(n+1) - 1. | [
"0",
"3",
"10",
"31",
"112",
"503",
"2786",
"18443",
"141744",
"1237755",
"12088266",
"130457479",
"1541023936",
"19769882767",
"273671845058",
"4065274481939",
"64493941507232",
"1088226653465139",
"19458541429154250",
"367527663494842671",
"7311506648705326672",
"152804399672163086695",
"3347034732868985727202",
"76675452816691696778843"
]
| [
"nonn"
]
| 24 | 0 | 2 | [
"A002104",
"A188545",
"A383922"
]
| null | Jianing Song, May 15 2025 | 2025-05-20T21:44:32 | oeisdata/seq/A383/A383922.seq | e2796d63d941eea7a82b1f62bd68aa5e |
A383923 | Numbers of the form m^p where both p and (m^(p^2) - 1)/(m^p - 1) are prime. | [
"4",
"8",
"16",
"27",
"36",
"100",
"196",
"256",
"400",
"512",
"576",
"676",
"1296",
"1331",
"1600",
"2916",
"3136",
"4356",
"5476",
"7056",
"8000",
"8100",
"8836",
"9261",
"12100",
"13456",
"14400",
"15376",
"15876",
"16900",
"17576",
"17956",
"21316",
"22500",
"24336",
"25600",
"27000",
"28900",
"30976",
"32400",
"33856",
"41616",
"42436",
"44100",
"50176",
"52900"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A383923",
"A383924",
"A383925",
"A383926"
]
| null | Max Alekseyev, May 15 2025 | 2025-05-18T02:29:29 | oeisdata/seq/A383/A383923.seq | fa9f0bbd519b93051e860f6765b59225 |
A383924 | Primes of the form (m^(p^2) - 1)/(m^p - 1) with a prime p, sorted with respect to the value of m^p. | [
"5",
"73",
"17",
"757",
"37",
"101",
"197",
"257",
"401",
"513",
"577",
"677",
"1297",
"1772893",
"1601",
"2917",
"3137",
"4357",
"5477",
"7057",
"64008001",
"8101",
"8837",
"85775383",
"12101",
"13457",
"14401",
"15377",
"15877",
"16901",
"308933353",
"17957",
"21317",
"22501",
"24337",
"25601",
"729027001",
"28901",
"30977",
"32401",
"33857",
"41617",
"42437",
"44101"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A383923",
"A383924",
"A383925",
"A383926"
]
| null | Max Alekseyev, May 15 2025 | 2025-05-18T02:29:47 | oeisdata/seq/A383/A383924.seq | d705b9f2b8102cc0720aa8827c87a86f |
A383925 | Primes of the form (m^(p^2) - 1)/(m^p - 1) with prime p and integer m >= 2. | [
"5",
"17",
"37",
"73",
"101",
"197",
"257",
"401",
"577",
"677",
"757",
"1297",
"1601",
"2917",
"3137",
"4357",
"5477",
"7057",
"8101",
"8837",
"12101",
"13457",
"14401",
"15377",
"15877",
"16901",
"17957",
"21317",
"22501",
"24337",
"25601",
"28901",
"30977",
"32401",
"33857",
"41617",
"42437",
"44101",
"50177",
"52901",
"55697",
"57601",
"62501",
"65537",
"67601",
"69697"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A383923",
"A383924",
"A383925",
"A383926"
]
| null | Max Alekseyev, May 15 2025 | 2025-05-18T02:30:09 | oeisdata/seq/A383/A383925.seq | b9f43ddb946ab8b66554e5f06d8d319d |
A383926 | Powers m^p with prime p, producing primes (m^(p^2) - 1)/(m^p - 1) in A383925. | [
"4",
"16",
"36",
"8",
"100",
"196",
"256",
"400",
"576",
"676",
"27",
"1296",
"1600",
"2916",
"3136",
"4356",
"5476",
"7056",
"8100",
"8836",
"12100",
"13456",
"14400",
"15376",
"15876",
"16900",
"17956",
"21316",
"22500",
"24336",
"25600",
"28900",
"30976",
"32400",
"33856",
"41616",
"42436",
"44100",
"50176",
"52900",
"55696",
"57600",
"62500",
"65536",
"67600",
"69696"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A383923",
"A383924",
"A383925",
"A383926"
]
| null | Max Alekseyev, May 15 2025 | 2025-05-18T02:30:22 | oeisdata/seq/A383/A383926.seq | 20b48263a8560fb9097da1ebb94df306 |
A383927 | Binary echo numbers: positive integers k such that the gpf(k-1) is a suffix of k when gpf(k-1) and k are written in binary. | [
"7",
"15",
"19",
"21",
"55",
"61",
"63",
"71",
"101",
"115",
"127",
"155",
"157",
"163",
"181",
"255",
"273",
"295",
"301",
"331",
"349",
"351",
"365",
"487",
"501",
"541",
"573",
"585",
"599",
"631",
"687",
"711",
"723",
"741",
"781",
"817",
"827",
"901",
"1055",
"1135",
"1211",
"1277",
"1331",
"1361",
"1387",
"1405",
"1459",
"1471",
"1475",
"1501",
"1621",
"1641",
"1751"
]
| [
"nonn",
"base"
]
| 17 | 1 | 1 | [
"A006530",
"A383296",
"A383896",
"A383927"
]
| null | Michael S. Branicky, May 15 2025 | 2025-05-23T10:19:09 | oeisdata/seq/A383/A383927.seq | 09b3fae8f51cde507c78b21a5fbd146a |
A383928 | Expansion of g.f. cosh(9*arctanh(4*sqrt(x))). | [
"1",
"648",
"76896",
"4601088",
"194102784",
"6662320128",
"199818854400",
"5451206492160",
"138644854013952",
"3341194489757696",
"77151510667984896",
"1720777996555517952",
"37293854107184922624",
"788969931176505507840",
"16350749459194860011520",
"332885987884833366343680",
"6673058165121160335851520"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 2 | [
"A285043",
"A285044",
"A285045",
"A285046",
"A383928"
]
| null | Karol A. Penson, May 15 2025 | 2025-05-18T07:41:48 | oeisdata/seq/A383/A383928.seq | ee69784bc90d287a166fef170773cdb0 |
A383929 | a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n, k) * (n-k)^(3*n). | [
"1",
"1",
"60",
"16626",
"12640320",
"20421928750",
"60233972198400",
"293230314199497444",
"2192804991244707840000",
"23869875368184417393486678",
"362747302615636095725568000000",
"7442995512384107947406685870219196",
"200637069747857913587015560318156800000",
"6945549555749361962465324588957867814958924"
]
| [
"nonn"
]
| 6 | 0 | 3 | [
"A002674",
"A298851",
"A383916",
"A383929",
"A383930"
]
| null | Vaclav Kotesovec, May 15 2025 | 2025-05-16T07:29:58 | oeisdata/seq/A383/A383929.seq | 404d5230e511fa3992b711101c169426 |
A383930 | a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n, k) * (n-k)^(5*n). | [
"1",
"1",
"1020",
"14152314",
"1071646712640",
"286802348769420190",
"209974096349134108992000",
"355016116241074708829385321492",
"1228958111984894631846657261766656000",
"7960240318398277162915923478914410838135990",
"89961580311571094335785117669395413813764096000000"
]
| [
"nonn"
]
| 7 | 0 | 3 | [
"A002674",
"A298851",
"A383917",
"A383929",
"A383930"
]
| null | Vaclav Kotesovec, May 15 2025 | 2025-05-16T07:29:54 | oeisdata/seq/A383/A383930.seq | 7542be78a9142257169ce5d40aeefdfb |
A383931 | Minimal nonnegative integer which reaches a cycle after exactly n iterations of the modified Sisyphus function of order 5 (A375208). | [
"613200",
"100123",
"100012",
"10",
"1023",
"100",
"0",
"10234",
"10000123",
"10000000000002"
]
| [
"nonn",
"base"
]
| 14 | 0 | 1 | [
"A308002",
"A352752",
"A375208",
"A383931"
]
| null | Matt Coppenbarger, May 15 2025 | 2025-05-29T00:15:18 | oeisdata/seq/A383/A383931.seq | 86a59b6e6c435c12c7ed405e1e57be09 |
A383932 | Integers k such that there exists an integer 0<m<k such that sigma(m)*sigma(k) = (m+k)^2. | [
"84",
"102",
"160",
"186",
"276",
"284",
"330",
"582",
"624",
"762",
"868",
"1164",
"1210",
"1372",
"1404",
"1446",
"1488",
"1540",
"1988",
"2156",
"2640",
"2716",
"2898",
"2924",
"3556",
"3708",
"3882",
"4074",
"4228",
"4536",
"5382",
"5564",
"5610",
"5802",
"6018",
"6282",
"6368",
"6392",
"6486",
"6612",
"6748",
"7140",
"7452",
"7494",
"7960",
"8358",
"8432",
"9222",
"9834"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A063990",
"A259180",
"A383239",
"A383483",
"A383484",
"A383932"
]
| null | S. I. Dimitrov, May 15 2025 | 2025-06-02T11:58:30 | oeisdata/seq/A383/A383932.seq | c554f458b96f9d0d81d593835b3127dc |
A383933 | Numbers k such that primorial base expansion of A276086(k) has the primorial base expansion of A003415(k) as its suffix, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function. | [
"0",
"1",
"2",
"6",
"26",
"95",
"122",
"185",
"206",
"1382",
"1919",
"2006",
"2285",
"2306",
"2966",
"4681",
"4841",
"5909",
"13961",
"14269",
"21446",
"30026",
"34249",
"37231",
"54589",
"54611",
"61459",
"90065",
"135229",
"145309",
"204566",
"217621",
"262099",
"266950",
"289621",
"306302",
"310939",
"341699",
"350099",
"353779",
"356809",
"358091",
"364361",
"496751",
"501289",
"503669",
"510506",
"515059"
]
| [
"nonn",
"base"
]
| 8 | 1 | 3 | [
"A003415",
"A049345",
"A276086",
"A276087",
"A383300",
"A383303",
"A383933"
]
| null | Antti Karttunen, May 15 2025 | 2025-05-15T17:11:45 | oeisdata/seq/A383/A383933.seq | 71d2ab9d06b4b1f2844a6bccc1cee265 |
A383940 | Consecutive states of the linear congruential pseudo-random number generator (25173*s+13849) mod 2^16 when started at s=1. | [
"1",
"39022",
"61087",
"20196",
"45005",
"3882",
"21259",
"65216",
"19417",
"30502",
"20919",
"26076",
"16421",
"44130",
"63139",
"32824",
"14513",
"51934",
"36303",
"35284",
"8573",
"11930",
"41787",
"65200",
"9865",
"29590",
"743",
"39628",
"46037",
"30162",
"47315",
"23080",
"30049",
"20814",
"4351",
"30916",
"22317",
"25098"
]
| [
"nonn",
"easy"
]
| 27 | 1 | 2 | [
"A096550",
"A096561",
"A383940",
"A384082",
"A384085",
"A384150",
"A384194",
"A384220"
]
| null | Sean A. Irvine, May 21 2025 | 2025-06-17T17:48:01 | oeisdata/seq/A383/A383940.seq | 73460a4bb693c139290c5c09c0af2ef8 |
A383956 | Consecutive states of the linear congruential pseudo-random number generator used by BASIC on the Poly-1 computer when started at 1. | [
"1",
"7771826",
"12906479",
"12752200",
"14370573",
"4177230",
"16102619",
"5888068",
"8967385",
"14199722",
"1838727",
"7559424",
"14513509",
"9092550",
"15771891",
"2282364",
"11580593",
"15929250",
"14479391",
"2474936",
"6872765",
"1998142",
"6754315",
"6251956",
"4652937",
"6660762",
"6157495",
"1357168"
]
| [
"nonn",
"easy"
]
| 21 | 1 | 2 | [
"A096550",
"A096561",
"A383956"
]
| null | Sean A. Irvine, May 15 2025 | 2025-05-25T20:48:31 | oeisdata/seq/A383/A383956.seq | a3faea7683d2e131f91bf55487af91ca |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.